Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering

Hybrid deep modeling of a CHO-K1 fed-batch process: combining first-principles with deep neural networks

Introduction: Hybrid modeling combining First-Principles with machine learning is becoming a pivotal methodology for Biopharma 4.0 enactment. Chinese Hamster Ovary (CHO) cells, being the workhorse for industrial glycoproteins production, have been the object of several hybrid modeling studies. Most previous studies pursued a shallow hybrid modeling approach based on three-layered Feedforward Neural Networks (FFNNs) combined with macroscopic material balance equations. Only recently, the hybrid modeling field is incorporating deep learning into its framework with significant gains in descriptive and predictive power. Methods: This study compares, for the first time, deep and shallow hybrid modeling in a CHO process development context. Data of 24 fed-batch cultivations of a CHO-K1 cell line expressing a target glycoprotein, comprising 30 measured state variables over time, were used to compare both methodologies. Hybrid models with varying FFNN depths (3-5 layers) were systematically compared using two training methodologies. The classical training is based on the Levenberg-Marquardt algorithm, indirect sensitivity equations and cross-validation. The deep learning is based on the Adaptive Moment Estimation Method (ADAM), stochastic regularization and semidirect sensitivity equations. Results and conclusion: The results point to a systematic generalization improvement of deep hybrid models over shallow hybrid models. Overall, the training and testing errors decreased by 14.0% and 23.6% respectively when applying the deep methodology. The Central Processing Unit (CPU) time for training the deep hybrid model increased by 31.6% mainly due to the higher FFNN complexity. The final deep hybrid model is shown to predict the dynamics of the 30 state variables within the error bounds in every test experiment. Notably, the deep hybrid model could predict the metabolic shifts in key metabolites (e.g., lactate, ammonium, glutamine and glutamate) in the test experiments. We expect deep hybrid modeling to accelerate the deployment of high-fidelity digital twins in the biopharma sector in the near future.

Machine learning in fermentative biohydrogen production: Advantages, challenges, and applications

Hydrogen can be produced in an environmentally friendly manner through biological processes using a variety of organic waste and biomass as feedstock. However, the complexity of biological processes limits their predictability and reliability, which hinders the scale-up and dissemination. This article reviews contemporary research and perspectives on the application of machine learning in biohydrogen production technology. Several machine learning algorithems have recently been implemented for modeling the nonlinear and complex relationships among operational and performance parameters in biohydrogen production as well as predicting the process performance and microbial population dynamics. Reinforced machine learning methods exhibited precise state prediction and retrieved the underlying kinetics effectively. Machine-learning based prediction was also improved by using microbial sequencing data as input parameters. Further research on machine learning could be instrumental in designing a process control tool to maintain reliable hydrogen production performance and identify connection between the process performance and the microbial population.

About Model Validation in Bioprocessing

In bioprocess engineering the Qualtiy by Design (QbD) initiative encourages the use of models to define design spaces. However, clear guidelines on how models for QbD are validated are still missing. In this review we provide a comprehensive overview of the validation methods, mathematical approaches, and metrics currently applied in bioprocess modeling. The methods cover analytics for data used for modeling, model training and selection, measures for predictiveness, and model uncertainties. We point out the general issues in model validation and calibration for different types of models and put this into the context of existing health authority recommendations. This review provides a starting point for developing a guide for model validation approaches. There is no one-fits-all approach, but this review should help to identify the best fitting validation method, or combination of methods, for the specific task and the type of bioprocess model that is being developed.

Hybrid Models for Efficient Control, Optimization, and Monitoring of Thermo-Chemical Processes and Plants

This paper describes a procedure and an IT product that combine numerical models, expert knowledge, and data-based models through artificial intelligence (AI)-based hybrid models to enable the integrated control, optimization, and monitoring of processes and plants. The working principle of the hybrid model is demonstrated by NOx reduction through guided oscillating combustion at the pulverized fuel boiler pilot incineration plant at the Institute for Technical Chemistry, Karlsruhe Institute of Technology. The presented example refers to coal firing, but the approach can be easily applied to any other type of nitrogen-containing solid fuel. The need for a reduction in operation and maintenance costs for biomass-fired plants is huge, especially in the frame of emission reductions and, in the case of Germany, the potential loss of funding as a result of the Renewable Energy Law (Erneuerbare-Energien-Gesetz) for plants older than 20 years. Other social aspects, such as the departure of experienced personnel may be another reason for the increasing demand for data mining and the use of artificial intelligence (AI).

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.

An intracellular signaling pathway is often represented by a set of nonlinear ordinary differential equations, which translate our current knowledge about the signaling pathway into a testable mathematical model. However, predictions from such models are often subject to high uncertainty since many signaling pathways are only partially known beforehand. In this study, we propose a systematic approach to develop a hybrid model to improve model accuracy by combining machine learning and the first-principle modeling. Specifically, model correction terms are learned from discrepancy between model predictions and measurements, and these terms are added to the first-principle model to enhance the prediction accuracy. Once these correction terms are learned from the data, an artificial neural network (ANN) model is developed to find an empirical relation between the model and the correction terms so that the developed ANN can be used to posses improved predictive capabilities even in new operating conditions (i.e., generalizability). The final hybrid model is then constructed by coupling the first-principle model with the developed ANN.

Impact of profiling technologies in the understanding of recombinant protein production

Since expression profiling methods have been available in a high throughput fashion, the implication of these technologies in the field of biotechnology has increased dramatically. Microarray technology is one such unique and efficient methodology for simultaneous exploration of expression levels of numerous genes. Likewise, two-dimensional gel electrophoresis or multidimensional liquid chromatography coupled with mass spectrometry are extensively utilised for studying expression levels of numerous proteins. In the field of biotechnology these highly parallel analytical methods have paved the way to study and understand various biological phenomena depending on expression patterns. The next phenomenological level is represented by the metabolome and the (metabolic) fluxome. However, this chapter reviews gene and protein profiling and their impact on understanding recombinant protein production. We focus on the computational methods utilised for the analyses of data obtained from these profiling technologies as well as prominent results focusing on recombinant protein expression with Escherichia coli. Owing to the knowledge accumulated with respect to cellular signals triggered during recombinant protein production, this field is on the way to design strategies for developing improved processes. Both gene and protein profiling have exhibited a handful of functional categories to concentrate on in order to identify target genes and proteins, respectively, involved in the signalling network with major impact on recombinant protein production.

Large-scale production and purification of VLP-based vaccines

Virus-like particles (VLPs) hold tremendous potential as vaccine candidates. These innovative biopharmaceuticals present the remarkable advantages of closely mimicking the three-dimensional nature of an actual virus while lacking the virus genome packaged inside its capsid. As a result, an equally efficient but safer prophylaxis is anticipated as compared to inactivated or live attenuated viral vaccines. With the advent of successful cases of approved VLP-based vaccines, pharmaceutical companies are indeed redirecting their resources to the development of such products. This paper reviews the current choices and trends of large-scale production and purification of VLP-based vaccines generated through the baculovirus expression vector system using insect cells.

Hybrid metabolic flux analysis: combining stoichiometric and statistical constraints to model the formation of complex recombinant products

Background

Stoichiometric models constitute the basic framework for fluxome quantification in the realm of metabolic engineering. A recurrent bottleneck, however, is the establishment of consistent stoichiometric models for the synthesis of recombinant proteins or viruses. Although optimization algorithms for in silico metabolic redesign have been developed in the context of genome-scale stoichiometric models for small molecule production, still rudimentary knowledge of how different cellular levels are regulated and phenotypically expressed prevents their full applicability for complex product optimization.

Results

A hybrid framework is presented combining classical metabolic flux analysis with projection to latent structures to further link estimated metabolic fluxes with measured productivities. We first explore the functional metabolic decomposition of a baculovirus-producing insect cell line from experimental data, highlighting the TCA cycle and mitochondrial respiration as pathways strongly associated with viral replication. To reduce uncertainty in metabolic target identification, a Monte Carlo sampling method was used to select meaningful associations with the target, from which 66% of the estimated fluxome had to be screened out due to weak correlations and/or high estimation errors. The proposed hybrid model was then validated using a subset of preliminary experiments to pinpoint the same determinant pathways, while predicting the productivity of independent cultures.

Conclusions

Overall, the results indicate our hybrid metabolic flux analysis framework is an advantageous tool for metabolic identification and quantification in incomplete or ill-defined metabolic networks. As experimental and computational solutions for constructing comprehensive global cellular models are in development, the contribution of hybrid metabolic flux analysis should constitute a valuable complement to current computational platforms in bridging the metabolic state with improved cell culture performance.

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

Background

This paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.

Results

The proposed hybrid modelling methodology was evaluated using two case studies. The first of these deals with dynamic modelling of transcriptional factor A in mammalian cells. The protein transport from the cytosol to the nucleus introduced a delay that was accounted for by discrete time series formulation. The second case study focused on a simple network with distributed time delays that demonstrated that the discrete time delay formalism has broad applicability to both discrete and distributed delay problems.

Conclusions

Significantly better prediction qualities of the novel hybrid model were obtained when compared to dynamical structures without time delays, being the more distinctive the more significant the underlying system delay is. The identification of the system delays by studies of different discrete modelling delays was enabled by the proposed structure. Further, it was shown that the hybrid discrete delay methodology is not limited to discrete delay systems. The proposed method is a powerful tool to identify time delays in ill-defined biochemical networks.